Empirical relationship ML-MD for the volcanic area of Mt. Etna (Italy)Empirical relationship ML-MD for the volcanic area of Mt. Etna (Italy)

Istanbul, Turkey

Studies on seismicity at Mt. Etna are of extreme importance for the high seismic and volcanic risk
which characterizes the area. In this region, seismic events are mainly located at less than 5 km b.s.l.
depth, producing arrivals with medium-to low-frequency content and/or complicated signatures at
stations just a few kilometers distant from the epicentral area (Patanè and Giampiccolo, 2004); on the
other hand, earthquakes which present high frequency content and sharp arrivals, similar to those of
typical earthquakes of tectonic areas, are mainly located between 5 and 20 km.
Seismicity mainly occurs in the form of swarms, whereas foreshock-mainshock-aftershock
sequences are rarely recorded, and seldom exceed magnitude 4.0 (Ferrucci and Patanè, 1993).
The calculation of the local magnitude ML is more objective than that of MD because the
measurement of the signal amplitude is less ambiguous with respect to the decay of the earthquake
coda, which may be masked by the presence of noise, volcanic tremor, or other shocks (Del Pezzo and
Petrosino, 2001; D'Amico and Maiolino, 2005). Therefore, since relationships adopted to estimate MD
and ML for Mt. Etna region do not produce the same results, it is mandatory to adopt an empirical
conversion to produce a homogeneous catalogue. Moreover, different magnitude scales strongly
influence the slope of the frequency-magnitude distribution. In particular, comparing the a- and bvalue
of the Gutenberg-Richter, different results are obtained.
The Standard Linear Regression (SLR) is the simplest and most commonly used regression
procedure applied in literature to carry out MD-ML relationship (e.g. Gasperini and Ferrari, 2000;
Gasperini, 2002; Bindi et al., 2005; Braunmiller et al., 2005). Its application without checking whether
its basic requirements are satisfied may lead to wrong results (Castellaro et al., 2006).
As an alternative it is better to use General Orthogonal Regression (GOR) relation (Carrol and
Ruppert, 1996), which assume a different uncertainty for each of the two variables (Lolli and
Gasperini, 2012).
The application of GOR methods requires the estimate of the ratio  between the dependent
and the independent variable variances, and when only the ratio variance is known, the GOR
represents the simplest and mostly used approach.
A database of magnitude observations recorded at Mt. Etna during the period 2005 – 2012 is
adopted for this study. The new ML-MD relationship obtained by applying the GOR is:
1.237 0.009 0.483 0.016 L D M M (1)
with a correlation coefficient R=0.90 and rms between observed and calculated ML of 0.27. The
superiority of the GOR relation over the SLR has been demonstrated on the basis of the best fitting
between regression line and data distribution.
The ML-MD relationship obtained by GOR significantly reduces the previous bias between ML
and MD estimated for earthquakes recorded at Mt. Etna and will be used for the purpose of catalogue
homogenization. Conversely, the commonly used SLR may induce systematic errors in magnitude
conversion, introducing apparent catalogue incompleteness, as well as a heavy bias in estimates of the
slope of the frequency–magnitude distribution. All this can be avoided by using the GOR in magnitude
conversions.